11 March, 2016

Spurious correlation!

Number of Nicholas Cage Movies
Drownings by Falling into a Swimming Pool

From: tylervigen.com.

Standard statistical methods applied to general time series might not work.

Cointegration extends regression methods to cover more cases.

I'll talk about implementation of solution methods.


Generating model

I(0) time series are formally expressed

Vector of n most recent values

Integration order

A series xt is called I(1) if


The I(1) vector xt is cointegrated if there exists a vector β such that

An autoregressive model

Simplified. The VECM extends this.

Cointegration from this view

The I(1) series xt has cointegration rank 1 if

Rank r cointegration of k series

Require each series to be I(1).

α, β full column rank


   ... and Haiku

A very drunk man. Out walking his faithful dog. Cointegration.